Transfer-matrix approach for finite-difference time-domain simulation of periodic structures

Area of Science:

• Photonics
• Computational Electromagnetics
• Materials Science

Background:

• The transfer-matrix method is crucial for analyzing optical properties of periodic structures.
• Traditional frequency-domain calculations involve complex linear algebra.
• Existing methods have limitations for certain complex structures and incidence conditions.

Purpose of the Study:

• To present a novel technique for calculating the transfer matrix using the finite-difference time-domain (FDTD) method.
• To demonstrate the implementation of this FDTD-based transfer matrix calculation.
• To validate the technique by calculating transmittance spectra of photonic crystal slabs.

Main Methods:

• Development of an FDTD-based algorithm for transfer matrix computation.
• Implementation of the algorithm within an existing FDTD code.
• Calculation of transmittance spectra for opal photonic crystal slabs with spherical scatterers.

Main Results:

• Successfully calculated the transfer matrix using the FDTD method.
• Obtained accurate transmittance spectra for multi-layered photonic crystal slabs.
• Demonstrated the versatility of the technique for various photonic structure analyses.

Conclusions:

• The FDTD-based transfer matrix calculation is an effective alternative to traditional methods.
• This technique enhances the analysis of periodic structures, including photonic crystals.
• The method offers potential for advanced applications like photonic band structure calculations and oblique incidence analysis.